My translation is not very literary, but focued on understanding of you "patrons".
Comment 1: For "library card" there are several words in russian:
"formulyar" (формуляр) - used by professional librarians,
"kartochka" (карточка) - used in common life for all sorts of cards.
I used "formulyar", but you may use any of them.
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"I'm sorry, but no one here speaks Russian." - "Sozhaleyu, no zdes nikto ne govorit po russki" - "Сожалею, но здесь никто не говорит по русски".
"Would you like to open a new library card?" - "Ne zhelaete zavesti novyi formulyar?" - "Не желаете завести новый формуляр?"
"We'll need one proof of address, like a driver's license or a bill addressed to your home." - "Nam ponadobitsya podtverzhdenie vashego adresa, naprimer voditelskie prava ili kvitantsiya (or schot) na oplatu" - "Нам понадобится подтверждение вашего адреса, например, водительские права или квитанция (или счёт) на оплату"
"You have a new card, so you can only take out three items today. But next time you can take out a lot more." - "U vas novyi formulyar, poetomu vyi vjzhete vzyat segodnya tolko tri knigi (books) / predmeta (other things)" - "У вас новый формуляр, поэтому вы можете взять сегодня только три книги / предмета".
"I'm sorry, but you can only take out (###) items like that." - "Sozhaleyu, no vyi mozhete vzyat tolko ### takikh knigi (books) / predmeta (other things)" - "Сожалею, но вы можете взять только ### таких книги / предмета".
"You have an overdue book and owe (###) on it. You can still take out books, but you'll need to pay the fine." - "U vas prosrochennyie knigi i dolg ### za nikh. Vyi eshe mozhete brat knigi, no vyi dolzhnyi zaplatit shtraf" - "У вас просроченные книги и долг ### за них. Вы ещё можете брать книги, но вы должны заплатить штраф".
"This will be due back in three weeks." - I didn't get it. Is it an order (instruction, direction) or an informing?
"We only have Russian items on VHS and cassette. Do you have a VHS or cassette player?" - "Russkie u nas tolko na VHS ili na kassetakh" - "Русские у нас только на VHS или на кассетах". ("Do you have a VHS or cassette player?" - doesn't need in this situation. They can sum "2+2".)
"You can use the computer for one hour a day." - "Vyi mozhete ispolzovat komp'uter odin chas v den" - "Вы можете использовать компьютер один час в день".
"Enter your library card number here, and your name here." - "Vvedite nomer formulyara zdes, i svoyo imya zdes" - "Введите номер формуляра здесь и своё имя здесь".
"Are you familiar with our English classes? Would you be interested?" - Hmm... "English classes" - is it a course of training in The English language?
"Do you go to English classes at Lutheran Services?" - most russians are stalwart supporters of Orthodoxy
)
"Would you like to meet someone about English classes?" - I didn't get the situation.
"Please give me your name and phone number, or a time when you can come to the library at night when someone who speaks Russian can meet with you." - "Pozhaluysta, dayte mne vashi imya i telefon ili soobshite vremya, kogda vyi smozhete priyti vecherom, chtobyi kto-to russkogovoryashiy smog vstretit vas" - Пожалуйста, дайте мне ваши имя и телефон, или сообщите время, когда вы сможете прийти вечером, чтобы кто-то русскоговорящий смог встретить вас". Hm.. I think it's vere unusual situation.
